Children's Spatial Skills Seen as Key to Math Learning

Preschools and kindergartens long have taught children "task skills," such as cutting paper and coloring inside the lines. But new research suggests the spatial and fine-motor skills learned in kindergarten and preschool not only prepare students to write their mathematics homework neatly, but also prime them to learn math and abstract reasoning.

"We think of early-childhood classrooms as being really high in executive-function demands, but what children are being asked to exercise [executive function] on end up being visual-motor and fine-motor tasks," said Claire E. Cameron, a research scientist at the University of Virginia's Center for Advanced Study of Teaching and Learning, in Charlottesville. She spoke at a forum held here last week by the Needham, Mass.-based Learning and the Brain Society.

Put yourself in the mind of a 4- or 5-year-old, and copying a shape on the blackboard onto a piece of paper is a much more cognitively complex task than it is for an adult: Understanding the design, then holding that shape in your mind and deciding how to start copying, requires working memory, one of the brain's executive functions. Gripping the pencil properly, applying the right pressure to avoid tearing the paper, and keeping the paper oriented on the desk all need fine-motor skills that also, at such ages, require focus and self-control.

"Children learning to write have not automated these skills," Ms. Cameron said. "Even sitting up straight so you can face the paper can be difficult."

Children deemed "typically developing" can still show a wide range of visual-motor skills. In one test, children are asked to draw increasingly complex shapes.

Copying Patterns

As part of the Minds in Motion project at the University of Virginia, researchers test how well preschool and early-elementary children copy simple designs. The student drawings here were done by children without disabilities who were of the same age but different levels of development in executive-function and fine-motor skills.

Original Works

Students' Interpretations

SOURCE: Claire E. Cameron

"Some kids are actually seeing parts that aren't there," Ms. Cameron said, noting one attempt at a cross that looks more like an abstract animal.

"This is a normal developmental state," she said. "When we copy something, we have a mental image and we are manipulating it and coordinating what you see with your movements."

Other researchers at the University of Virginia center have found executive function, fine-motor skills, and general knowledge in kindergarten are better predictors of 8th grade reading and math achievement than early-literacy skills.

Moreover, the black-white achievement gap in elementary school also may have some of its roots in those foundational skills: Black children studied by the center entered kindergarten on average 9½ months developmentally younger than their white classmates in executive function and 8 months developmentally younger in visuo-spatial skills, though it's not yet known why.

Researchers led by David W. Grissmer, a research professor at the university, found 1st graders who had attended high-poverty preschools often had never built with construction paper, blocks, or modeling clay.

Precursor for Math

And, in a separate, ongoing study of nearly 500 preschoolers, Ms. Cameron found about a third tested high in both executive-function skills—such as following directions amid distractions—and visual-motor skills, such as cutting paper. Children who performed well in either or both executive-function and visual-motor skills achieved well in both math and reading achievement and class behavior later on in the early-elementary grades.

"It's the children who are low in both who are struggling," Ms. Cameron said. The more quickly children become automatic in mentally coordinating an action or repeating a design, the more they can free up working memory and organize their thinking for more abstract problems.

As part of a $1 million pilot project supported by the National Institute of Child Health and Human Development, Mr. Grissmer and his team worked with after-school programs at three high-poverty, high-minority elementary schools in Charleston, S.C.

For 45 minutes a day, four days a week, for seven months in fall 2010 and spring 2011, groups of five to seven kindergartners and 1st graders played games that required them to copy designs and shapes. At the start of each class, the pupils took part in "calirobics"—handwriting and line-tracing exercises set to music. During the rest of the class they copied a pattern or picture in a variety of materials. Some days, students cut and pasted construction paper to make chains or built models out of clay or Lego blocks; other days, they used stencils, pattern blocks, or fusible plastic beads.

The children were not taught any math, and the teachers did not draw any links between the art projects and math skills, but by spring, the 1st graders showed significant improvement in both math and executive-function skills.

At the start of the program, the students had tested at the 30th percentile nationwide in numeracy and "applied problems" on a standardized test of early math knowledge; by the end of the program, they had moved to the 47th percentile in those areas. The participating students showed similarly large improvements in looking, listening, attention, and executive-function skills.

The development of fine-motor coordination and executive function may be more critical than subject content for early-childhood classrooms, Mr. Grissmer said.

"We start kids too early on math and reading when they don't have these foundational skills," he said. In the earliest grades, he said, "you can't just teach reading and math to get higher reading and math skills."

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